ON THE κ-REGULAR SEQUENCES AND THE GENERALIZATION OF F-MODULES Ahmadi-Amoli, Khadijeh; Sanaei, Navid;
For a given ideal I of a Noetherian ring R and an arbitrary integer , we apply the concept of -regular sequences and the notion of -depth to give some results on modules called -Cohen Macaulay modules, which in local case, is exactly the -modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any -regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any -regular sequence is at most . Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.